Question

How do you use the fundamental identities to simplify `1/(tan^2x+1)`?

Answer 1

see below

Explanation:

Use identities: `tan^2x+1=sec^2x` and `sec x = 1/cosx`

`1/(tan^2x+1) = 1/sec^2 x=1/(1/cos^2x)=1*cos^2x/1 = cos^2 x`